Investment and Pricing with Spectrum Uncertainty: A Cognitive Operator's Perspective

This paper studies the optimal investment and pricing decisions of a cognitive mobile virtual network operator (C-MVNO) under spectrum supply uncertainty. Compared with a traditional MVNO who often leases spectrum via long-term contracts, a C-MVNO can acquire spectrum dynamically in short-term by both sensing the empty "spectrum holes" of licensed bands and dynamically leasing from the spectrum owner. As a result, a C-MVNO can make flexible investment and pricing decisions to match the current demands of the secondary unlicensed users. Compared to dynamic spectrum leasing, spectrum sensing is typically cheaper, but the obtained useful spectrum amount is random due to primary licensed users' stochastic traffic. The C-MVNO needs to determine the optimal amounts of spectrum sensing and leasing by evaluating the trade off between cost and uncertainty. The C-MVNO also needs to determine the optimal price to sell the spectrum to the secondary unlicensed users, taking into account wireless heterogeneity of users such as different maximum transmission power levels and channel gains. We model and analyze the interactions between the C-MVNO and secondary unlicensed users as a Stackelberg game. We show several interesting properties of the network equilibrium, including threshold structures of the optimal investment and pricing decisions, the independence of the optimal price on users' wireless characteristics, and guaranteed fair and predictable QoS among users. We prove that these properties hold for general SNR regime and general continuous distributions of sensing uncertainty. We show that spectrum sensing can significantly improve the C-MVNO's expected profit and users' payoffs.Comment: A shorter version appears in IEEE INFOCOM 2010. This version has been submitted to IEEE Transactions on Mobile Computin

Optimal Pricing Effect on Equilibrium Behaviors of Delay-Sensitive Users in Cognitive Radio Networks

This paper studies price-based spectrum access control in cognitive radio networks, which characterizes network operators' service provisions to delay-sensitive secondary users (SUs) via pricing strategies. Based on the two paradigms of shared-use and exclusive-use dynamic spectrum access (DSA), we examine three network scenarios corresponding to three types of secondary markets. In the first monopoly market with one operator using opportunistic shared-use DSA, we study the operator's pricing effect on the equilibrium behaviors of self-optimizing SUs in a queueing system. %This queue represents the congestion of the multiple SUs sharing the operator's single \ON-\OFF channel that models the primary users (PUs) traffic. We provide a queueing delay analysis with the general distributions of the SU service time and PU traffic using the renewal theory. In terms of SUs, we show that there exists a unique Nash equilibrium in a non-cooperative game where SUs are players employing individual optimal strategies. We also provide a sufficient condition and iterative algorithms for equilibrium convergence. In terms of operators, two pricing mechanisms are proposed with different goals: revenue maximization and social welfare maximization. In the second monopoly market, an operator exploiting exclusive-use DSA has many channels that will be allocated separately to each entering SU. We also analyze the pricing effect on the equilibrium behaviors of the SUs and the revenue-optimal and socially-optimal pricing strategies of the operator in this market. In the third duopoly market, we study a price competition between two operators employing shared-use and exclusive-use DSA, respectively, as a two-stage Stackelberg game. Using a backward induction method, we show that there exists a unique equilibrium for this game and investigate the equilibrium convergence.Comment: 30 pages, one column, double spac

Cloud/fog computing resource management and pricing for blockchain networks

The mining process in blockchain requires solving a proof-of-work puzzle, which is resource expensive to implement in mobile devices due to the high computing power and energy needed. In this paper, we, for the first time, consider edge computing as an enabler for mobile blockchain. In particular, we study edge computing resource management and pricing to support mobile blockchain applications in which the mining process of miners can be offloaded to an edge computing service provider. We formulate a two-stage Stackelberg game to jointly maximize the profit of the edge computing service provider and the individual utilities of the miners. In the first stage, the service provider sets the price of edge computing nodes. In the second stage, the miners decide on the service demand to purchase based on the observed prices. We apply the backward induction to analyze the sub-game perfect equilibrium in each stage for both uniform and discriminatory pricing schemes. For the uniform pricing where the same price is applied to all miners, the existence and uniqueness of Stackelberg equilibrium are validated by identifying the best response strategies of the miners. For the discriminatory pricing where the different prices are applied to different miners, the Stackelberg equilibrium is proved to exist and be unique by capitalizing on the Variational Inequality theory. Further, the real experimental results are employed to justify our proposed model.Comment: 16 pages, double-column version, accepted by IEEE Internet of Things Journa

Multilevel Pricing Schemes in a Deregulated Wireless Network Market

Typically the cost of a product, a good or a service has many components. Those components come from different complex steps in the supply chain of the product from sourcing to distribution. This economic point of view also takes place in the determination of goods and services in wireless networks. Indeed, before transmitting customer data, a network operator has to lease some frequency range from a spectrum owner and also has to establish agreements with electricity suppliers. The goal of this paper is to compare two pricing schemes, namely a power-based and a flat rate, and give a possible explanation why flat rate pricing schemes are more common than power based pricing ones in a deregulated wireless market. We suggest a hierarchical game-theoretical model of a three level supply chain: the end users, the service provider and the spectrum owner. The end users intend to transmit data on a wireless network. The amount of traffic sent by the end users depends on the available frequency bandwidth as well as the price they have to pay for their transmission. A natural question arises for the service provider: how to design an efficient pricing scheme in order to maximize his profit. Moreover he has to take into account the lease charge he has to pay to the spectrum owner and how many frequency bandwidth to rent. The spectrum owner itself also looks for maximizing its profit and has to determine the lease price to the service provider. The equilibrium at each level of our supply chain model are established and several properties are investigated. In particular, in the case of a power-based pricing scheme, the service provider and the spectrum owner tend to share the gross provider profit. Whereas, considering the flat rate pricing scheme, if the end users are going to exploit the network intensively, then the tariffs of the suppliers (spectrum owner and service provider) explode.Comment: This is the last draft version of the paper. Revised version of the paper accepted by ValueTools 2013 can be found in Proceedings of the 7th International Conference on Performance Evaluation Methodologies and Tools (ValueTools '13), December 10-12, 2013, Turin, Ital